This talk presents forthcoming work on the analysis of HDG methods in finite element exterior calculus (FEEC), applied to the the Hodge–Dirac and Hodge–Laplace problems on the de Rham complex. In particular, we show that equal-order HDG methods with O(1) penalties achieve optimal-order convergence given suitable elliptic regularity.
Joint work with Calvin Reedy and Marston Xue